Two angles are supplementary if the sum of their measures is 180 degrees. Given the measures of the angles:
- m∠QRS = (x + 40)°
- m∠SRT = x°
Since the angles are supplementary, we have the equation:
\[ m∠QRS + m∠SRT = 180° \]
Substituting the expressions for the angles:
\[ (x + 40) + x = 180 \]
Now, combine like terms:
\[ 2x + 40 = 180 \]
Next, subtract 40 from both sides:
\[ 2x = 140 \]
Then, divide by 2:
\[ x = 70 \]
Now that we have the value of \( x \), we can find the measure of ∠QRS:
\[ m∠QRS = x + 40 = 70 + 40 = 110° \]
Thus, the measure of ∠QRS is \( 110° \).